On Reality and Models

I discuss the relations among four worlds: reality, mathematical models, computer simulation, and models of computation. Pros and cons of two models of computation, the Turing machine and the real number model, are presented. Then the intrinsic difficulty of solving a mathematical model, as measured by its computational complexity, is discussed. In the concluding section I'll consider the example of protein-folding and apply what we've learned to present some possible reasons for the dissonances in our current state of knowledge.